Consider a cell of 10 μ radius, R: area 4·πR2,
volume 4/3·πR3 →
we have a volume to area ratio of R/3 = 10/3 μm = 3300 nm
this means that for every square nm of membrane we have 3300 nm3 of volume
At -100 mV, 16 nm2 of membrane host 1 ion, but correspond to 3300·16 nm3 and therefore about 50,000 cations.
This means that 1 ion out of 50,000 that moves through the membrane produces a 100 mV displacement of membrane potential!
The figure represents the submembrane microdomain: any ion that enters or exits will rapidly mix in the solution,
without changing to any significant extent the concentrations, but markedly affecting the membrane potential.
The cell is imagined to start with equal solutions on the two sides.
The pump extrudes 3 Na+ and imports 2 K+, with a net extrusion of 1 positive charge.
This imbalances the charges and generates a negative internal potential.
This also reduces intracellular Na+ concentration.
The extra K+ can exit more easily than the Na+ can reenter (about 40× permeability ratio).
Every K ion that exits in excess of the Na ions that enter produces further charge imbalance and membrane potential.
This membrane potential counterbalances the further tendency of K+ to exit.
This simulation shows wide fluctuations of K+ concentration ratio and membrane potential - because few ions are considered,
but one can see that the system tends to stabilize around -80 mV (migth be different for different conductances or activity of the pump),
a K+ concentration ratio close to 40 (0.025), which would correspond to an equilibrium potential of about -96 mV.
The potential stabilizes around -80 because a little leak Na+ conductance (about 1/40 of K+ conductance) is there: